# Mathematical Analysis (MAT310)

The course covers fundamentals of mathematical analysis with focus on complex analysis.

Course description for study year 2024-2025. Please note that changes may occur.

Facts

MAT310

1

10

Autumn

1

Autumn

English

Time table

## Content

NB! This is an elective course and may be cancelled if fewer than 10 students are enrolled by August 20th for the autumn semester.

Elements of mathematical logic, basic topological notions, analytic and harmonic functions of a complex variable, Cauchy-Riemann conditions, Cauchy's integral theorem and integral formulas, Taylor and Laurent series representations, classification of isolated singularities and residue theory.

## Learning outcome

Upon completing this course students should be able to:

• Clearly understand what is meant by a mathematical proof, and how to communicate mathematical arguments clearly in the form of a mathematical proof.
• Understand basic topological notions (closed, open, connected and compact sets, convergence, continuity).
• Get operational knowledge of analytic and harmonic functions, including maximum principle and integral representations.
• Determine Taylor and Laurent series of elementary analytic functions, find their zero points and singularities, and get knowledge of residue theory and its applications.

## Required prerequisite knowledge

MAT100 Mathematical Methods 1

## Recommended prerequisites

MAT200 Mathematical Methods 2, MAT210 Real and Complex Calculus, MAT300 Vector Analysis

## Course coordinator:

Helge Paul Ruddat

## Method of work

6 hours lectures/problem solving per week.

## Open for

Admission to Single Courses at the Faculty of Science and Technology
Mathematics and Physics - Five Year Integrated Master's Degree Programme
Exchange programme at Faculty of Science and Technology

## Course assessment

There must be an early dialogue between the course supervisor, the student union representative and the students. The purpose is feedback from the students for changes and adjustments in the course for the current semester.In addition, a digital subject evaluation must be carried out at least every three years. Its purpose is to gather the students experiences with the course.

## Literature

The syllabus can be found in Leganto